Question

A) A 1.0 kg ball is located at the origin and a 2.0 kg ball is at
1.0 m away in the x-direction. Where is the center of mass of these
two balls.
(Answer in ihat + jhat+ khat form)

B) A 3.0 kg ball is located at (x,y,z)=(0,1.0,0)m and a 4.0 kg ball
is located at (1.0,1.0,0) m. Where is the center of mass of these
two balls?
(Answer in ihat + jhat+ khat form)

C) Where is the center of mass of all four balls? Determine this
two ways: (1) find the center of mass of all four balls treated
individually and then (2) find the center of mass acting as if the
system was made up of two bodies located at the two centers of
masses you found above (e.g. a total mass of 1 kg + 2 kg at the
location of the first center of mass you found above). The two
results should agree.
(Answer in ihat + jhat+ khat form)

D) Now, let's say that three identical, uniform rods, each 1.00 m
long, are welded perpendicular to one another at a common end so as
to represent the positive x-, y-, and z-axes of a Cartesian
coordinate system. Where is the CM of this object?
(Answer in jhat+ khat form)